Special CAMP: Penned to Flatland: New Class of Strongly-Coupled Topological Solutions at the Interface

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What happens when quantum particles are strongly coupled and “live” in different dimensions (like 3D and 2D)? Despite the seeming simplicity of this physics question, no accurate solution has been given so far. Compared to photonic crystals where some polariton modes were found most recently to be protected states – making the light confined, for example, to the crystal boundary ­– the topological nature of a “normal” 2D-polariton has not been fully addressed. This gap will be closed in my talk. In fact, a distinct family of non-perturbative solutions, corresponding to quantum modes confined at the dimension boundary, can be identified. For example, the 3D-continuum “absorbs” the discontinuity introduced by strong quantum coupling with flatland-polarization-modes and “ejects” new states, topologically distinct, to hybridize with the 2D modes. Such crossiton hybrid states could be expected to show unusual properties: indeed, the coupling continuously morphs the crossiton from a regular (non-topological) 2-level state into a Fano-mode, with abnormal spectral shape and dynamics.

This general approach is not specific to the 3D/2D interface and applies to a wide range of quantum-mechanical problems (e.g., Fano-Anderson problem: 0D/1D, or charge transport via a quantum constriction: 1D/2D) and recently studied quantum optics systems (e.g., hybrid plasmonic modes between photon continuum and low-D materials). Finally, for those enjoying deep theory, an exact analytical result in arbitrary dimensions will be outlined with the help of a new efficient method of solving coupled harmonic Dyson equations.